At the time of writing this column, the Ukrainian city of Lviv is under attack by the Russian army, but it still serves as a link between your country and the rest of Europe. The metropolis of 700,000, which was once Polish (Lwów) and Austro-Hungarian (Lemberg), does not often make international headlines, but has a rich history of more than 750 years.
Lviv also holds a special place in the annals of science, having been home, in the 1930s, to one of the most brilliant schools of mathematics Europe has ever seen, with stars such as H. Steinhaus, S. Banach, K. Kuratowski, J. Schauder , S. Mazur, K. Borsuk, S. Ulam and M. Kac, among others. It’s a tale of two cafes.
The tale begins at Café Roma, close to the university. It was there that the group gathered after the weekly meetings of the Polish Mathematical Society, for hours of discussion on set theory, general topology, functional analysis, and other topics, over a cup of tea or coffee. Thus, a collaborative environment was forged that seems natural today, but was unusual in mathematical research at the time.
Although consumption at the Café was frugal, it was not always easy to pay the bill, especially towards the end of the month… One day, upset with the difficulty in obtaining credit at Roma, Banach decided to move the meeting to the Café Escocês, the 20 meters away, where the group continued collaborating in solving mathematical problems.
Ulam says that the tables had marble tops, where it was possible to write directly with pencils. But Banach’s wife didn’t like this mess, so in 1935 she provided a large notebook for them to write down problems and solutions so they wouldn’t be forgotten. The Scottish Book, as it became known, is an almost legendary mathematical document.
It contains two hundred formulated problems, of which about 1/4 are still unsolved. The notebook was kept in the Café, under the care of a waiter who brought it to the tables whenever requested. There were prizes for solving some problems. Number 153, for example, was solved in 1972 by the Swede Per Enflo, who thus earned the award: a live goose, which Mazur financed and personally delivered to him in a televised ceremony throughout Poland.
Next week I will continue talking about Lviv and the Scottish Book.
